For the Schwarzschild geometry we get the trivial (everywhere in the acceptable domain of coordinates) value of the shear tensor. One may wonder how we have got the value of the shear viscosity (REF ) if \(\sigma _{ab}\)  is presented in (REF ) just formally. The value of the shear viscosity can not be fixed from \(\eta \sigma _{ab}=0\)  equation in this case that requires taking additional arguments. For instance, it could be the structure of (projected) Einstein equations that allows one to rewrite them in the form of Navier-Stokes-like equations (Damour-Navier-Stokes (DNS) equations) [1]}, [2]}, [3]}. Then, the effective shear viscosity can be extracted from the structure of the DNS equations.
